A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line Failure

TL;DR

This paper develops a stochastic dynamical model using large deviation theory and a Markov process to simulate and analyze cascading transmission line failures in power systems, validated against numerical simulations.

Contribution

It introduces a novel kinetic Monte Carlo approach based on large deviation principles for simulating cascading failures in power grids.

Findings

The Markov model reproduces power-law cascade distributions.

Analytical expressions for line failure rates are derived and validated.

The approach extends to realistic power system settings.

Abstract

In this work, cascading transmission line failures are studied through a dynamical model of the power system operating under fixed conditions. The power grid is modeled as a stochastic dynamical system where first-principles electromechanical dynamics are excited by small Gaussian disturbances in demand and generation around a specified operating point. In this context, a single line failure is interpreted in a large deviation context as a first escape event across a surface in phase space defined by line security constraints. The resulting system of stochastic differential equations admits a transverse decomposition of the drift, which leads to considerable simplification in evaluating the quasipotential (rate function) and, consequently, computation of exit rates. Tractable expressions for the rate of transmission line failure in a restricted network are derived from large deviation theory arguments and validated against numerical simulations. Extensions to realistic settings are considered, and individual line failure models are aggregated into a Markov model of cascading failure inspired by chemical kinetics. Cascades are generated by traversing a graph composed of weighted edges representing transitions to degraded network topologies. Numerical results indicate that the Markov model can produce cascades with qualitative power-law properties similar to those observed in empirical cascades.